# Let P0,1i, Prl10, uxl P310,1 be 3 a Find the...

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CONCORDIA UNIVERSITY f)epartrnent of Mathematics & Statistics Cor:rse N{rrthcnlatics Nutrber 204 Section(s) ALL (except EC) Exarnination frin:rL Date April 2016 Pages 2 Irstructor All Course Examiners E CoLen Special Insiructions > Orrly appr_o\.ed caLculal,ors ai-e allowed: D' JrLstify aJ1 your auswers > All questiots have erlu::r.l valuc. 1. Lrsilg Gauss Jorcla[ utet]rorl, flncl ail solutiors of tlle lollowing systen of equations rr + 2:t:2 xr + 4x2 '- )q+3a2- 2. Let II : (a) !-ird (b) CalcuLate the rrratrix C so that MC: B, where B: J:j + Ia:5 3rl 3rs : 6 zl l- 4r.r : 8 /:;l\ \ r ,, o / 3. (a) Use Ctamer's n e to solr'e the fo1lo\\'ir1g system x\ + 2t:2 l3x3 ar+r3 rft + .12 rt I 'br Err'u,'r rh, ' 'r; 'rr ' , ' r" .r 'l - | Let -C be the line vith paralretric equaticrlls ,j : 2 1, : (1, 1. f.). li'incl vectors 1N1) t 2 srlch that u : 1r1 to ,c and ur is perPendicular to ,C. :Ilt,z:4*2tandlet ard such thai ul is parallel of eqn rt?\ \r r/ ations: li) 4. 12 20 -t 0 21 -t, lt + ti,2,
MATH 204 Final Exarn June 2015 Page 2 of 2 5. Let P](0,1.i), Pr(l.1.0), uxl P3(1.0,1) be 3 (a) Find the area of poirtts P2' P3'
(b) Fir.rd the equation of the plarte contairing P1, , 6. Lei I be the lirie with parametric equatioils z'-3 -t. g: -11:2t,::1-4f let P be the Plarre 41 29 P2, P3 and - 22 : 6 (a) Prove that, arrd 2 are pamllel' (b) Find tbe distarce between a rrd 2 7. Let,q: [1,2.3) andur: ( 1,2' 1) (a) Fird scalars a ancl 6 such l\al aq I btt2: (0' {,2) (b) Fincl a vector ,3 such that t'1 ) 1j2 . ,i is a ba'sis oi lR3 ' Find a b:rsis for the solution /r r. u l o 6 \ 8. lrA loo,roz ]"r'JX' \o l n o I + / ['] space of the homogeteous systen / X = (l /11 \ I Le ,a . f ,1 | ) l '-d J.l erpPnj uas ^l 'r' \/ Is ,4 dingonalizablei If yes. lind P so that P-LAP : D cliagonal' ro L.rA I I ]). rinn r" \J z,/ d copvrBht d thq ploreer(t v